Question-2

Let \(v_{1}=(1,1),v_{2}=(1,0)\) and \(v_{3}=(0,1)\) be three vectors. Compute the following:

• \(2v_{1}+0v_{2}+v_{3}\)

• \(0v_{1}+2v_{2}+3v_{3}\)

• \(2v_{1}+v_{2}+0v_{3}\)

• \(0v_{1}+3v_{2}+2v_{3}\)

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We use the fact that \(0\cdot(a,b)=(0,0)\) for all \(a,b\in\mathbb{R}\). Now we can go ahead and compute these quantities:

\[ \begin{aligned} 2v_{1}+v_{3} & =2(1,1)+(0,1)=(2,3)\\ 2v_{2}+3v_{3} & =2(1,0)+3(0,1)=(2,3)\\ 2v_{1}+v_{2} & =2(1,1)+(1,0)=(3,2)\\ 3v_{2}+2v_{3} & =3(1,0)+2(0,1)=(3,2) \end{aligned} \]